We can use the formula for calculating the z-score to determine how many standard deviations a player's height is above the mean. The formula for the z-score is:

$z = \frac{x - \mu}{\sigma}$

where:

• $z$ is the z-score,
• $x$ is the value (player's height),
• $\mu$ is the mean height,
• $\sigma$ is the standard deviation.

In this case, we are given the player's z-score of $z = 4.81$. The z-score represents how many standard deviations the player's height is above or below the mean. Since the z-score is already provided as 4.81, this means:

$\text{The player's height is 4.81 standard deviations above the mean.}$

So, the player's height is 4.81 standard deviations above the mean.

Would you like a breakdown of the formula or further explanation?

Here are 5 related questions to expand on this:

1. How is the z-score interpreted in relation to probability distributions?
2. If the player's height was 2 standard deviations above the mean, what would his z-score be?
3. How can you calculate the mean and standard deviation from a given set of data?
4. What does a negative z-score indicate about a value in relation to the mean?
5. How can z-scores help in comparing values from different distributions?

Tip: Z-scores allow you to compare data points from different distributions by standardizing them in terms of their relative position to the mean.